交叉加劲钢板深梁弹性屈曲分析

以交叉加劲钢板深梁为研究对象,利用有限元软件ANSYS分析其弹性屈曲性能,讨论了抗弯刚度比、跨高比、钢板深梁厚度对其弹性屈曲性能的影响;考虑钢板深梁在钢框架的弯剪受力特性,根据板的经典理论建立了交叉加劲钢板深梁屈曲荷载计算公式,提出了等效屈曲系数。结果表明:交叉加劲钢板深梁的临界屈曲荷载随抗弯刚度比增大而增大,但达到门槛刚度比后,增大幅度急剧减小,得到门槛刚度比约为10;临界屈曲荷载随跨高比和板厚的减小而减小,等效屈曲系数随板厚减小而增大;等效屈曲系数与跨高比关系曲线由二次抛物线形向波浪形渐变,交叉加劲钢板深梁受力特性由剪切主导向弯曲主导过渡。     

钢筋混凝土矩形薄板在弹性地基上的热屈曲

基于板的小挠度理论,考虑混凝土材料的非线性,推导了弹性地基上钢筋混凝土矩形薄板在热载作用下的平衡方程和稳定方程,给出了四边简支钢筋混凝土矩形薄板在均匀温度变化时临界屈曲温度变化的封闭解,讨论了板的材料常数、长宽比、相对厚度和基床系数等对临界屈曲温度变化的影响,从而为工程结构中弹性地基上钢筋混凝土矩形薄板的临界屈曲温度的计算提供了理论计算依据。     

非均匀受压矩形钢管混凝土局部弹性屈曲分析

应用不同的特征函数描述了矩形板在非均匀压力作用下的屈曲形态,解决了采用三角级数为屈曲函数模拟非均匀受压荷载作用下单侧表面约束矩形板件屈曲模态的不对称问题;通过伽辽金法建立屈曲控制方程组,分析了非均匀荷载作用对矩形钢管混凝土构件局部弹性屈曲性能的影响。结果表明:钢管屈曲系数随着不均匀荷载梯度α增加而增大,纯弯作用下（α=2）的板件弹性屈曲荷载特征值约为轴压作用下的6倍;钢板的宽厚比限值随不均匀加载梯度α的增大而增加;非均匀荷载作用下非加载边固支约束板件的屈曲系数明显大于简支约束的板件。     

反对称层合板屈曲性态分析

应用屈曲控制方程，导出了反对称层合板在面内双向压缩下的屈曲方程，计算了相应的临界荷载并讨论了层合角对临界应力的影响，分析表明层合角对材料的临界应力有较大的影响。     

开口肋加劲板屈曲模态与临界屈曲应力分析

为更好掌握开口肋加劲板的设计计算方法,采用弹性稳定分析方法,对无纵向和横向加劲肋的四边简支板、纵向加劲肋等间距布置的四边简支加劲板、纵向和横向加劲肋等间距布置的加劲板进行屈曲模态和临界屈曲应力分析。结果表明:对于四边简支板或四边简支加劲板,临界屈曲应力与板宽、板长和板厚均有关,减小板宽和板长以及增大板厚可提高临界屈曲应力;随着加劲肋刚度比的变化,四边简支加劲板一般表现出3种屈曲模态,模态1为加劲肋与被加劲板共同发生整体屈曲,模态2为在加劲肋处形成波节,加劲肋与被加劲板发生屈曲,模态3为加劲肋为刚性加劲肋,不会发生失稳,只有被加劲板发生局部失稳;临界屈曲应力随加劲肋刚度比的增大而增大,模态1增大幅度最大,模态2次之,模态3逐步趋于定值。     

Axi-symmetrical deflection and buckling of circular porous-cellular plate

The main goal of this paper is a solution of the problem of buckling and deflection. A circular porous plate with simply supported edge under radial uniform compression and uniformly distributed load (pressure) is considered. Mechanical properties of the isotropic porous material vary across the thickness of the plate. Middle plane of the plate is its symmetry plane. A field of displacements (geometric model of nonlinear hypothesis) is described. The principle of stationarity of the total potential energy allowed to get a system of differential equations that govern the plate stability. A critical load and a deflection are determined. The results obtained for porous plates are compared to homogeneous circular plates.     

Tripping of thin-walled stiffeners in the axially compressed stiffened panel with lateral pressure

Tripping of stiffeners in stiffened panels under combined loads of axial force and lateral pressure is studied. Firstly, on the basis of the Vlasov's differential equation for torsional buckling of thin-walled bars, a generalized eigenvalue problem for tripping of stiffeners is derived by using the Galerkin's Method. Then the effect of the lateral pressure (dead load) to the critical axial stress (live load) upon tripping is investigated by solving the eigenvalue problem. The rotational restraint provided by the plate is taken into account. The effects of the compressive stress in the plate and the plate buckling mode are also discussed. Finally, an approximate equation to estimate the critical tripping stress with the effect of the lateral pressure is proposed. After some modifications, it can be applied in design rules for the purpose of checking the tripping strength of the stiffeners.     

Uncertainty propagation in dynamics of composite plates: A semi-analytical non-sampling-based approach

In this study, the influences of spatially varying stochastic properties on free vibration analysis of composite plates were investigated via development of a new approach named the deterministic-stochastic Galerkin-based semi-analytical method. The material properties including tensile modulus, shear modulus, and density of the plate were assumed to be spatially varying and uncertain. Gaussian fields with first-order Markov kernels were utilized to define the aforementioned material properties. The stochastic fields were decomposed via application of the Karhunen-Loeve theorem. A first-order shear deformation theory was assumed, following which the displacement field was defined using admissible trigonometric modes to derive the potential and kinetic energies. The stochastic equations of motion of the plate were obtained using the variational principle. The deterministic-stochastic Galerkin-based method was utilized to find the probability space of natural frequencies, and the corresponding mode shapes of the plate were determined using a polynomial chaos approach. The proposed method significantly reduced the size of the mathematical models of the structure, which is very useful for enhancing the computational efficiency of stochastic simulations. The methodology was verified using a stochastic finite element method and the available results in literature. The sensitivity of natural frequencies and corresponding mode shapes due to the uncertainty of material properties was investigated, and the results indicated that the higher-order modes are more sensitive to uncertainty propagation in spatially varying properties.     

Analysis on local thermal critical buckling of square concrete filled steel short tubular under axial compression

基于薄板小挠度理论，采用能量法对方钢管混凝土中钢板局部热屈曲性能进行了理论分析。推导了热力耦合作用下钢管混凝土中钢板的临界屈曲系数，并给出了相应的钢板临界屈曲温度计算公式；推导了钢管混凝土外包钢板在热力耦合作用下外荷载、热荷载与常温临界屈曲荷载的关系。结果表明：钢管的弹性模量对临界屈曲温度没有影响；宽厚比对临界屈曲系数及临界屈曲温度有较大影响,并建议了宽厚比限值；通过热屈曲临界系数求得构件屈曲时长宽比的最小值，可用于钢板热屈曲设计。     

Analytical buckling analysis of an inflatable beam made of orthotropic technical textiles

An analytical approach was considered to study the buckling and the behavior of an inflatable orthotropic beam subjected to uniform compression loads under different boundary conditions. In order to assess the stability of inflatable structures, it is necessary to evaluate the critical load of the inflatable components in their pressurized configurations. First, a 3D inflatable orthotropic beam model based on the Timoshenko's kinematics was briefly introduced: the nonlinearities (finite rotation, follower forces) were included in this model. The nonlinear equilibrium equations were derived from the total Lagrangian form of the virtual work principle: the linearized equations were then obtained. By solving these linearized equations, an analytical expression of the critical buckling load was obtained. This critical buckling load was investigated through several load cases with several boundary conditions. The discrepancy due to the orthotropic character between the present model and the isotropic models found in the literature was evaluated, as well as the influence of the inflation pressure and the fabric mechanical properties on the value of critical load. The buckling mode shapes were also determined. To check the limit of validity of the results, the wrinkling load was also presented in every case.     

钢桥塔内部通行孔选型及有限元分析

钢桥塔内部通行孔对受压壁板力学性能产生不利影响。基于有限元分析,研究不同孔洞形状和孔洞大小对单轴受压开孔板弹性应力分布、弹性屈曲和弹塑性屈曲三方面性能的影响。结果表明:除圆孔外的其他各种孔型板,孔洞形状对开孔板弹性屈曲应力和弹塑性极限强度影响不大,但其对应力集中系数影响较大,其中,圆角矩形孔、长圆形孔和椭圆形孔板的应力集中系数较低。实际情况中,圆角矩形孔和长圆形孔板是钢桥塔内部通行孔的首选。但当孔径较大时,应采取孔洞补强措施来保证大孔径板件的力学性能满足设计要求。     

Elastoplastic buckling of circular annular plates under uniform in-plane loading

This paper deals with the elastoplastic buckling of a circular annular plate, with various axially symmetric boundary conditions and uniform axially symmetric in-plane radial loads on the inner and outer edge. The analysis is based on the standard linear buckling equations and the material behaviour is modelled by the small strain J₂ flow and deformation theories of plasticity where an elastic linear hardening rheological model of the material is considered. The solutions are obtained using the equilibrium approach where the governing differential equation is solved by the finite difference method which leads to the determination of eigenvalues of a homogeneous system of linear equations. Elastoplastic buckling loads for axially symmetric and asymmetric buckling shape modes with m waves in the circumferential direction are calculated and compared for both theories of plasticity. For one case, an experiment was performed and the results were compared with theoretical predictions.     

Thermal buckling analysis of rectangular composite plates with temperature-dependent properties based on a layerwise theory

Thermal buckling analysis of rectangular composite multilayered plates under uniform temperature rise is investigated using a layerwise plate theory. von Karman strain–displacement equations are employed to account for large deflections occurrence. It is already proven that the layerwise theory results are compatible with the three-dimensional theory of elasticity results. The accuracy of the present results is increased by substituting each layer by many virtual sub-layers. The final governing equations are not simplified or linearized. Material properties are assumed to vary with temperature. Hermitian finite element formulation is used to ensure a C¹ continuity for the lateral deflections. No semi-analytic solution is employed to reduce the problem to an eigenvalue one. Layerwise formulations are usually displacement-based. Therefore, force or moment boundary conditions (e.g. simply supported boundary condition), are approximately satisfied. A FEM algorithm is presented to exactly incorporate the boundary conditions. A proposed numerical scheme and a modified Budiansky instability criterion presented by the author are used to determine the buckling temperature in a computerized solution. Finally, results of the present techniques are compared with the results of the high-order theories presented by some well-known researchers and the influences of various geometric and mechanical properties parameters of the composite plate on the buckling temperature are studied.     

两边连接交叉加劲钢板剪力墙弹性屈曲分析

采用ANSYS有限元软件对两边连接交叉加劲钢板剪力墙进行了弹性屈曲分析,重点研究了加劲肋与墙板的刚度比、墙板高厚比、边长比以及加劲肋宽厚比对弹性屈曲系数的影响,并将分析结果与十字加劲板进行了比较.研究表明,交叉加劲肋能够显著提高钢板剪力墙的弹性屈曲荷载,其远大于十字加劲肋;随着墙板边长比和高厚比的增大,屈曲系数趋于减小;而较小的加劲肋宽厚比能使墙板获得较大的屈曲系数;最后给出了两边连接交叉加劲板弹性屈曲系数的计算公式.     

T型组合受弯玻璃板的承载性能

针对应用于玻璃楼梯、玻璃楼板等承载玻璃结构中的T型组合受弯玻璃板,在特定的条件下结构会发生整体失稳而破坏,其承载力由屈曲荷载控制,而现有的玻璃幕墙规范中对这种结构形式没有相关规定的问题,采用有限元方法分析了不同参数对T型组合受弯玻璃板静力承载性能的影响,并对不同荷载状况下T型组合受弯玻璃板的稳定性问题进行分析,得到了其屈曲荷载及屈曲模态。计算结果表明:影响T型组合受弯玻璃板静力承载性能的主要因素为板厚、肋板高度和翼缘板宽度,而影响其稳定性的主要因素为肋板高度和翼缘板宽度的比值。     

Stochastic analysis of laminated composite plate considering stochastic homogenization problem

This paper discusses a multiscale stochastic analysis of a laminated composite plate consisting of unidirectional fiber reinforced composite laminae. In particular, influence of a microscopic random variation of the elastic properties of component materials on mechanical properties of the laminated plate is investigated. Laminated composites are widely used in civil engineering, and therefore multiscale stochastic analysis of laminated composites should be performed for reliability evaluation of a composite civil structure. This study deals with the stochastic response of a laminated composite plate against the microscopic random variation in addition to a random variation of fiber orientation in each lamina, and stochastic properties of the mechanical responses of the laminated plate is investigated. Halpin-Tsai formula and the homogenization theory-based finite element analysis are employed for estimation of effective elastic properties of lamina, and the classical laminate theory is employed for analysis of a laminated plate. The Monte-Carlo simulation and the first-order second moment method with sensitivity analysis are employed for the stochastic analysis. From the numerical results, importance of the multiscale stochastic analysis for reliability evaluation of a laminated composite structure and applicability of the sensitivity-based approach are discussed.     

相关屈曲对平面钢桁架柱屈曲性能的影响

利用ANSYS 14.0软件建立平面钢桁架柱模型,采用特征值屈曲分析和非线性分析方法模拟结构的整体屈曲、局部屈曲和相关屈曲（两种屈曲模式相互作用）.发现弦杆长细比对整体屈曲临界力PE和局部屈曲临界力P1的大小起控制作用,当PE＞P1时,屈曲模式的相互作用降低了结构的极限承载力;当PE＜P1时,屈曲模式的相互作用不仅降低了结构的极限承载力,还改变了结构的初始后屈曲性能.     

Thickness optimization of circular annular plate at buckling

This work deals with thickness optimization of a circular annular plate at buckling. The plate is loaded with uniform, axially symmetric, in-plane loads on the inner and outer edge. The variable thickness of the plate is approximated by a function of radial coordinates and design variables. An optimization problem is defined to find optimal sets of design variables which maximize buckling loads at constant weight/volume of the plate. The required buckling loads are determined according to the standard linear buckling equations, and the material is modelled by the small strain J₂ flow and deformation theories of plasticity where an elastic linear hardening rheological model is considered. Optimal thickness functions are determined for different support and load cases and the numerical results show that buckling loads can be increased significantly.     

开缝钢板墙抗震性能的试验研究

为了研究开缝形式对开缝钢板墙抗震性能的影响,完成了6组共12片1∶4比例的开缝钢板墙试件的往复加载试验。试验结果表明:开单层竖缝钢板墙的屈曲形态是竖缝间板带的单独扭转屈曲形态(第一类屈曲形态),屈服与破坏集中在竖缝的端部,造成竖缝间板带逐渐断裂,导致试件的刚度与承载力逐渐下降,滞回曲线出现剪切滑移现象;开双层竖缝钢板墙的屈曲是板内对角方向形成斜拉带的整板屈曲形态(第二类屈曲形态),到剪切位移角超过4%,试件的承载力没有出现下降,且滞回曲线相对饱满;竖缝间板带的长宽比越大,试件的抗侧刚度与屈服承载力越低;与开单层竖缝试件相比,开双层竖缝墙板的抗侧刚度与屈服承载力均明显提高。建议的试件初始刚度和承载力理论计算结果与试验得到的结果基本一致。     

Buckling of plate strip subjected to localised corrosion—a stochastic model

The paper deals with the effects of localised corrosion on the buckling load of a plate strip. A stochastic model of the problem is suggested and intact plate thickness, modulus of elasticity, corrosion loss of weight and position of corroded area of a chosen extent are assumed as basic random variables. The design values and the first three statistical moments of the critical loads are calculated and the results are referred to the upper bound of probability distribution of corrosion loss of weight. The numerical study employs data from the recent experimental research [Bull. Tech. Univ. Istanbul 47(1994) 423] and a relationship between stochastic and experimental results is drawn.